Computing intersection cardinality

ABSTRACT

A computer-implemented method for computing an intersection or an intersection cardinality of each pair of a set in a first list of a plurality of sets and a set in a second list of a plurality of sets, the method including calculating a first union of a predetermined number of sets in the first list, obtaining filtered sets of the second list by filtering out an element from the plurality of sets in the second list, the element being not included in the first union, and intersecting a set in the first list and a set in the filtered sets of the second list.

BACKGROUND Technical Field

The present invention relates to a method for computing an intersectioncardinality, and more specifically, to a method for computing anintersection or an intersection cardinality of each pair of a set in afirst list including plural sets and a set in a second list includingplural sets. The present invention is typically used for analyzing textdata

SUMMARY

According to an embodiment of the present invention, there is provided acomputer-implemented method for computing an intersection or anintersection cardinality of each pair of a set in a first list of aplurality of sets and a set in a second list of a plurality of sets. Themethod calculates a first union of a predetermined number of sets in thefirst list. The method obtains filtered sets of the second list byfiltering out an element from the plurality of sets in the second list,the element being not included in the first union. The method intersectsa set in the first list and a set in the filtered sets of the secondlist.

According to another embodiment of the present invention, there isprovided a computer-implemented method for computing an intersection oran intersection cardinality of each pair of a set in a first list of aplurality of sets and a set in a second list of a plurality of sets. Themethod calculates a first union of a predetermined number of sets in thefirst list. The method obtains filtered sets of the second list byfiltering out an element from the plurality of sets in the second list,the element being not included in the first union. The method calculatesa second union of a predetermined number of sets in the second list. Themethod obtains filtered sets of the first list by filtering out anelement from the plurality of sets in the first list, the element beingnot included in the second union. The method intersects a set in thefiltered sets of the first list and a set in the filtered sets of thesecond list.

According to still another embodiment of the present invention, there isprovided a system for computing an intersection or an intersectioncardinality of each pair of a set in a first list of a plurality of setsand a set in a second list of a plurality of sets. The system includes aprocessor and a memory coupled to the processor. The memory includesinstructions which, when executed by the processor, cause the processorto calculate a first union of a predetermined number of sets in thefirst list. The instructions further cause the processor to obtainfiltered sets of the second list by filtering out an element from theplurality of sets in the second list, the element being not included inthe first union. The instructions further cause the processor tointersect a set in the first list and a set in the filtered sets of thesecond list.

According to yet another embodiment of the present invention, there isprovided a computer program product for computing an intersection or anintersection cardinality of each pair of a set in a first list of aplurality of sets and a set in a second list of a plurality of sets. Thecomputer program product includes a computer readable storage mediumhaving program instructions embodied with the computer readable storagemedium. The program instructions are executable by a computer to causethe computer to calculate a first union of a predetermined number ofsets in the first list. The program instructions are executable by acomputer to further cause the computer to obtain filtered sets of thesecond list by filtering out an element from the plurality of sets inthe second list, the element being not included in the first union. Theprogram instructions are executable by a computer to further cause thecomputer to intersect a set in the first list and a set in the filteredsets of the second list.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing a computer system according to anembodiment.

FIG. 2 is a table showing correlation analysis according to theembodiment.

FIG. 3 is a table illustrating a calculation for correlation analysis oftarget words.

FIGS. 4A and 4B are tables showing correlation analysis according to theembodiment.

FIG. 5 is a flowchart of the operation of a data processing unit forcorrelation analysis according to the embodiment.

FIG. 6 is a table showing correlation analysis according to a secondembodiment.

FIG. 7 is a flowchart of the operation of a data processing unitaccording to the second embodiment.

FIG. 8 is a table showing correlation analysis according to a thirdembodiment.

FIG. 9 depicts a cloud computing node according to an embodiment.

FIG. 10 depicts a cloud computing environment according to anembodiment.

FIG. 11 depicts abstraction model layers according to an embodiment.

FIG. 12 is a diagram showing an example of a hardware configuration of acomputer able to implement the embodiment.

DETAILED DESCRIPTION

Hereinafter, embodiments of the present invention will be described indetail with reference to the attached drawings.

It is to be noted that the present invention is not limited to theseembodiments given below and may be implemented with variousmodifications within the scope of the present invention. In addition,the drawings used herein are for purposes of illustration.

FIG. 1 is a block diagram of a computer system 1 according to anembodiment. The computer system 1 performs an intersection or anintersection cardinality of each pair of a set in a first list of aplurality of sets and a set in a second list of a plurality of sets. Asshown in FIG. 1, the computer system 1 may include a data source 100, adata processing unit 300, and a data destination unit 500.

The data source 100 generates text data to be processed by the dataprocessing unit 300. For example, the data source 100 generates textdata based on microblogging data on the Internet, or based on voice dataof conversations between customers and operators in a call center. Inthe present embodiment, the data source 100 generates (stores) text datathat include multiple text datasets, namely multiple documents. In otherwords, the data source 100 generates a set of documents. Such a set ofdocuments may be a universal set, in this embodiment.

The data processing unit 300 may include a calculating unit 310, anobtaining unit 330, and an intersecting unit 350. These control blocksmay be programmed to be performed by a central processing unit (CPU).

The calculating unit 310 receives text data from the data source 100 tocalculate a union, namely to determine a sum, of multiple sets includedin a specific list. In other words, the calculating unit 310 stores thefirst list, and calculates the first union of sets in the first list.The first list will be described later.

The obtaining unit 330 filters out a specific element(s) from sets in aspecific list. In other words, the obtaining unit 330 stores the secondlist and filters out a specific element(s) from the sets in the secondlist to obtain the filtered second list. The second list and thefiltered second list will be described later.

The intersecting unit 350 intersects a set in the first list and a setin the filtered second list. In other words, the intersecting unit 350computes the intersection cardinality of each set of the first list andeach set of the filtered second list.

The data destination unit 500 is a recipient of the results of the dataprocessing by the data processing unit 300.

With the expansion of information processing technology, large amountsof diverse text data have recently been analyzed for new findings in awide variety of fields. Examples include the analysis of microbloggingdata, and voice data at a call center (hereinafter referred to as “callcenter data”).

Various approaches have been proposed for analyzing text data, such astext mining, which is a process of deriving findings from the text data.In the present embodiment, a correlation analysis between two words iscarried out, as one example of such approaches.

Hereinafter, the correlation analysis in the present embodiment will bedescribed in detail.

FIG. 2 is a table showing correlation analysis according to theembodiment. More specifically, the table of FIG. 2 shows a correlationof words included in call center data.

The call center data includes multiple text datasets (documents). Eachdocument includes the text of the conversation between a customer and anoperator. More specifically, each document is related to a customerfeedback regarding specific products (e.g. Product 1 to Product 4 inFIG. 2).

In this embodiment, the documents are respectively listed in the firstlist and the second list. Each of the first list and the second list isa list of sets, and each set consists of the documents having a targetword. Here, the target word is a word (term) selected for thecorrelation analysis. In other words, the target word is a word that hasa possibility of being included in the above multiple documents.

As shown in FIG. 2, the first list includes the sets of the documentsrespectively labeled with the target words, “Expensive” (C₁), “Late”(C₂), and “Damage” (C₃). Similarly, the second list includes the setsrespectively labeled with the target words, “Product 1” (B₁), “Product2” (B₂), “Product 3” (B₃), and “Product 4” (B₄). Note that “C₁”, “C₂”,“C₃”, “B₁”, “B₂”, “B₃” may be used in the following explanation,including other embodiments.

Here, the set C₁ is a subset consisting of the documents which includethe target word “Expensive”. The set C₁ may be obtained by C₁={Hit docIDs of “Expensive”}. Similarly, each of the sets C₂, C₃, B₁, B₂, B₃ andB₄ is a subset consisting of the documents which include the target word“Late”, “Damage”, “Product 1”, “Product 2”, “Product 3”, and “Product4”, respectively. It is to be noted that the sets C₁ to C₃ and the setsB₁ to B₄ are included in one universal set in this example.

Here, the target words of the first list and the second list may beselected by a user of the computer system 1. It is to be noted that thetarget words to be selected are not limited to those in the embodiment,and any word may be selected as the target word. For example, the targetword may be selected based on the appearance frequency of the word inthe call center data.

The intersection size of each pair of one set from the first list andone set from the second list is computed in the correlation analysis. Asshown in FIG. 2, each cell of the table shows the intersectioncardinality, namely hit count for the AND search query of the verticaland horizontal words. All cells in the table i.e. intersection sizes ofall combinations of the sets in the first list and the sets in thesecond list may be calculated.

The degree of correlation of the target words is determined based on thecount size of the intersection cardinality. For example, the count iscompared with a predetermined number to determine whether the targetwords are found to have a strong correlation.

Here, the intersection cardinality is calculated by |C_(k)∩B_(n)| foreach pair of C_(k) (k=1, 2, . . . , K, K≧2) and B_(n) (n=1, 2, . . . ,N, N≧2). For example, in FIG. 2, the intersection cardinality of the setC₁ and the set B₁, as denoted by |C₁∩B₁|, is 351. In other words, thecount size of the documents including the target words “Expensive” and“Product 1” is 351. Note that “C_(k)” and “B_(n)” may be used in thefollowing explanation, including other embodiments.

It is to be noted that|C_(k)∩B_(n)|=|(C_(k)∩C)∩B_(n)|=|C_(k)∩(C∩B_(n))|=|C_(k)∩B*_(n)|. “C” iscalculated by ∪_(k=1˜K) C_(k). In the example of FIG. 2, “C” is a unionof C₁ to C₃, i.e. C=C₁∪C₂∪C₃. “B*_(n)” represents a filtered setobtained from the set B_(n). Note that “C” and “B*_(n)” may be used inthe following explanation, including other embodiments.

Here, the set B*_(n) is obtained by filtering out one or more elements(documents) which are not included in the union C, from the set B_(n)and this filtering is performed by calculating C∩B_(n). In thisembodiment, such one or more filtered sets B*_(n) (n=1, 2, . . . , N,N≧2) constitute a filtered list (i.e. the filtered second list). Thatis, the filtered list is composed of one or more sets B*_(n) eachincluding the remaining element(s) after eliminating the element(s)which is not included in the union C. In other words, the filtered listis composed of one or more sets B*_(n) each only including theelement(s) which is in common with the element(s) included in the unionC.

In the present embodiment, |C_(k)∩B*_(n)| is calculated, instead of|C_(k)∩B_(n)|. The calculation of |C_(k)∩B*_(n)| enables to reduce acalculation load as compared to the calculation of |C_(k)∩B_(n)|.Hereinafter, an example of the reduction in the calculation load will bedescribed referring to FIG. 3.

FIG. 3 is a table illustrating a calculation for correlation analysis oftarget words. In the table of FIG. 3, “D” represents the universal setconsisting of Document 1 to Document 10. Documents 1 to 10 are examplesof the documents generated by the data source 100. It is to be notedthat “D” is a set of document IDs.

In FIG. 3, “B*₁”, which is an example of the filtered sets of the secondlist, represents the filtered set obtained from the set B₁. “B*₁” iscalculated by C∩B₁, as shown in FIG. 3. Further, the cross mark in eachcell in FIG. 3 indicates that the target word is included in any one ofDocuments 1 to 10.

If the calculation of |C_(k)∩B₁| is applied, the calculations forDocuments 1, 3, 6, 7 and 10 are carried out. However, if the calculationof |C_(k)∩B*₁| is applied, the calculations for only Documents 1 and 7are carried out. In other words, the calculations for Documents 3, 6 and10 (indicated by the cross marks circled with dotted line) can beomitted by applying the calculation of |C_(k)∩B*₁|, in this example.This enables to reduce the calculation load, or enables to quicklycalculate the intersection cardinality.

FIGS. 4A and 4B are tables showing correlation analysis according to theembodiment. Hereinafter, the detailed process for the correlationanalysis will be described with reference to FIGS. 4A and 4B.

In the example of FIG. 4A, the sets in the first list are sorted inorder of size (i.e. the number of the documents contained in each set),more specifically, |C₁|≧|C₂|≧ . . . ≧|C_(K)|. Similarly, the sets in thesecond list are sorted in order of size, more specifically, |B₁|≧|B₂|≧ .. . ≧|B_(N)|.

In the present example, the correlation analysis is carried outaccording to the following calculations (1) to (4).

(1) The sets C_(k) (k=1, 2, . . . , K) in the first list are dividedinto G groups (C₁, . . . , (C_(i[1])), (C_(i[1]+1), . . . , C_(i[2])), .. . , (C_(i[G−1]+1), . . . , C_(i[G])), where (i[0]=0, i[G]=K,i[g]>i[g−1] for g=1, . . . , G). The size of g-th group i[g]−i[g−1] willbe described later.

Hereinafter, one divided group of C_(i[g−1]+1), . . . C_(i[g]) isdenoted by the divided group A of the sets A₁, . . . , A_(M), as shownin FIG. 4B. The calculation for the correlation analysis of the sets(A₁, . . . , A_(M)) in the divided group A and the sets (B₁, . . . ,B_(N)) in the second list will be explained below.

(2) The first union is calculated. The first union is a union of pluralsets in the divided group A and may be calculated by A=∪_(m=1˜M) A_(m).

(3) The filtered sets B*₁, B*₂, . . . , B*_(n) in the second list arecomputed by A∩B_(n) (n=1, . . . , N). More specifically, the specificelement(s) is filtered out from the sets in the second list.

(4) The intersection cardinality is computed. More specifically, theintersection cardinality of each set in the divided group A in the firstlist and each set in the second filtered list is calculated by|A_(m)∩B*_(n)|.

It is to be noted that the above calculation (2) takes time to calculate|D|/w and Σ_(m=1˜M)|A_(m)|, where |D| represents the number of elementsin the universal set D consisting of Document 1 to Document 10 in thisexample, and “w” represents the machine word length, i.e. digitizedcapability of the CPU. The time of the calculation (2) is proportionalto M. Similarly, the above calculation (3) takes time to calculateΣ_(n=1˜N)|B_(n)|, and the time of calculation (3) is proportional to N.

Thus, the calculations (2) and (3) may be overhead. However, thecalculations (2) and (3) are one-time cost for all B₁, . . . , B_(N), toreduce their size by |A|/|D|, which accelerates the computation for allM×N pairs.

Hereinafter, an implementation and a time complexity for thecalculations (2), (3), and (4) will be described. It is to be noted thata constant is omitted in the following explanation.

First, the calculation (2) may include calculations (2-A), (2-B), and(2-C). The calculation (2-A) is to create bit sets for A₁, . . . ,A_(M). The time complexity of the calculation (2-A) may be calculated byM|D|/w. The calculation (2-B) is to put values of A₁, . . . , A_(M). Thetime complexity of the calculation (2-B) may be calculated byΣ_(m=1˜M)|A_(M)|. The calculation (2-C) is to get ∪_(m=1˜M) A_(m) bybit-wise OR. The time complexity of calculation (2-C) may be calculatedby M|D|/w.

Similarly, the calculation (3) is to compute B*_(n)=A∩B_(n) (n=1, . . ., N). The time complexity of the calculation (3) may be calculated byΣ_(n=1˜N)|B_(n)|. The calculation (4) is to compute |A_(m)∩B*_(n)|. Thetime complexity of the calculation (4) may be calculated byMΣ_(n=1˜N)|B*_(n)|, and approximated by MΣ_(n=1˜N)|B_(n)∥A|/|D|.

Here, provided that a=|A₁|, b=|B₁|, α, β, γ, δ>0, the time forA_(m)∩B_(n) is T(M)≦α|D|/(Nw)+βa/N+γb/M+δabM/|D|. The right side of theequation takes its minimum α|D|/(Nw)+βa/N+2(γδ)^(1/2)(a/|D|)^(1/2)b atM=(γ/δ)^(1/2)(|D|/a)^(1/2). Practically, 2(γδ)^(1/2)(a/|D|)^(1/2)b isdominant (Java), and a/|D| can be seen as an improvement factor(acceleration factor).

Here, the group size of the g-th group i[g]−i[g−1] will be described.The group size of the g-th group i.e. the number of the sets included inthe g-th group may be any number. In the present embodiment, the groupsize of the g-th group, or the combination of plural sets for thecomputation of the first union is selected such that the expected sizeof a union of all sets in the g-th group (e.g. the size of g-th groupi[g]−i[g−1]) is sufficiently smaller than the number of elements in theuniversal set (e.g. |D|), and sufficiently larger than the size of eachset in the g-th group (e.g. |C_(i[g−1]+1)|). In other words, theexpected size of a union of all sets in the g-th group may be determinedbased on the number of elements in the universal set and the size ofeach set in the g-th group.

Here, in the present embodiment, the group size is selected such thatthe group size is proportional to (|D|/|C_(i[g−1]+1)|)^(1/2). In otherwords, the combination of plural sets for the computation of the firstunion is selected such that the number of the sets is proportional tothe inverse of the square root of the size ratio of the representativevalue of the sizes of the sets (|C_(i[g−1]+1)|) to the number ofelements in the universal set (|D|). In other words, the number ofelements in the universal set corresponds to the number of all possibleelements of each set. Note that the set in the g-th group is a subset ofthe universal set D so that the elements of the universal set D have apossibility of constituting the set in the g-th group. Namely, theelement in the universal set is a possible element of each set.

It is to be noted that the division of the first list C_(k) (k=1, 2, . .. , K) into G groups enables a reduction of a distribution of A₁ toA_(M) and thus an appropriate size of the union can be obtained.However, such division can be omitted. In other words, the first unionmay be composed of all sets included in the first list. Further, in theabove description, C_(i[g−1]+1), which is the largest in the g-th group,is selected as the representative vale of the size of the target group(the g-th group in the above example). Alternatively, an average of theg-th group, or other values may be selected as such representativevalue.

FIG. 5 is a flowchart of the operation of the data processing unit 300for correlation analysis according to the embodiment. Hereinafter, theoperation of the data processing unit 300 for the correlation analysiswill be described with reference to FIG. 5.

In the present example, the calculating unit 310 calculates the firstunion of a predetermined number of sets in the first list (step 501).Then, the obtaining unit 330 obtains filtered sets of the second list byfiltering out one or more elements from the plurality of sets in thesecond list (step 502). Wherein, the one or more elements are elementsnot included in the first union. Subsequently, the intersecting unit 350intersects each set in the first list and each set in the filtered setsin the second list obtained by the obtaining unit 330 (step 503).

Hereinafter, the operation for the correlation analysis according toanother embodiment (second embodiment) will be described with referenceto FIG. 6. FIG. 6 is a table showing correlation analysis according to asecond embodiment.

In the first embodiment, the calculation using one filtered list (thesecond filtered list) for the correlation analysis is conducted. Thisalgorithm may be called a “horizontal filtering”. On the other hand, thecalculation using a combination of filtered lists is conducted in thesecond embodiment. More specifically, in addition to the calculation ofB*_(n), filtered sets A*_(m) are also calculated. The filtered setsA*_(m) are examples of the filtered sets of the first list. Hereinafterthis algorithm may be called a “block filtering”.

The calculation of the second embodiment is basically the same as theabove calculations (1) to (3) of the first embodiment.

However, in the calculation (1), the sets in the second list may also bedivided into plural groups. It is to be noted that the division can beomitted.

Further, instead of the above calculation (4) of the first embodiment,the following calculations (5), (6), and (7) are conducted.

The calculation (5) is to compute “the second union” of plural sets inthe second list by B=∪_(n=1˜N) B*_(n). The calculation (6) is to filterout the element(s) which is not included in the second union from pluralsets in the first list. More specifically, the calculation (6) computesthe filtered sets A*_(m)=A_(m)∩B (m=1, . . . , M). The calculation (7)is to return |A*_(m)∩B*_(n)|.

Then, the operation of the data processing unit 300 in the secondembodiment will be described with reference to FIG. 7. FIG. 7 is aflowchart of the operation of the data processing unit 300 according tothe second embodiment.

In the present embodiment, the calculating unit 310 calculates the firstunion of a predetermined number of sets in the first list (step 701).The obtaining unit 330 obtains filtered sets of the second list byfiltering out one or more elements element from the plurality of sets inthe second list (step 702). Wherein, the one or more elements areelements not included in the first union. Then, the calculating unit 310calculates the second union of a predetermined number of sets in thesecond list (step 703). Subsequently, the obtaining unit 330 obtainsfiltered sets of the first list by filtering out one or more elementsfrom the plurality of sets in the first list (step 704). Wherein, theone or more elements are elements not included in the second union.Then, the intersecting unit 350 intersects the filtered sets in thefirst list and the filtered sets in the second list obtained by theobtaining unit 330 (step 705).

In the above description, the horizontal filtering and the blockfiltering for the correlation analysis have been explained. It is to benoted that the algorithm for the correlation analysis may be changedbased on a property of the text data. For example, the applied algorithmmay be switched based on the size of the first list and the second list.

Hereinafter, the operation for the correlation analysis according tostill another embodiment (third embodiment) will be described withreference to FIG. 8. FIG. 8 is a table showing correlation analysisaccording to the third embodiment.

As shown in FIG. 8, the first list is divided into several groups,including the first group (C₁, . . . , C_(J)) and the h-th group (C_(P),. . . , C_(Q)). In the third embodiment, depending on the number of thesets included in each group, i.e. group size M_(g), the algorithm isselected from the horizontal filtering, the block filtering and BitSetmethod. BitSet method is to intersect each element (each cell of thetable) in C_(k) with a bitset (set) of B. Here, the bitset is a seriesof bits in the memory, and each bit corresponds to the element of B_(n).

In the third embodiment, if the group size M_(g) of a target group (e.g.the first group, the h-th group) of the first list is small (e.g.M_(g)=2), or smaller than a predetermined number, BitSet method iscarried out. On the other hand, if the group size M_(g) of the targetgroup is large, or larger than a predetermined number, the horizontalfiltering or the block filtering is carried out.

Similarly, the algorithm may be selected from the horizontal filteringand the block filtering, depending on the group size N_(g) of the groupof the second list. More specifically, if the group size N_(g) of agroup of the second list is small, or smaller than a predeterminednumber, the horizontal filtering is carried out. If the group size N_(g)of the target group is large, or larger than a predetermined number, theblock filtering is carried out.

Here, the parameters M_(g) and N_(g) may be calculated byM_(g)=0.5|D|/|A₁|^(1/2), and N_(g)=0.5|D|/|B₁|^(1/2). For example, theabove predetermined number (threshold) for M_(g) for switching thealgorithms may be set to 4. Also, the predetermined number (threshold)for N_(g) may be set to 10. In this example, if M_(g)<4, BitSet methodmay be selected, if M_(g)≧4 and N_(g)<10, the horizontal filtering maybe selected, and if M_(g)≧4 and N_(g)≧10, the block filtering may beselected.

It is to be noted that if the combination that is appropriate forcomputing the union cannot be found, the horizontal filtering (or blockfiltering) may not be selected, or may be prohibited from beingselected. An example of such appropriate combination is that theexpected size of the union of the combination is sufficiently smallerthan the number of all the possible elements and sufficiently largerthan the size of each set.

The descriptions of the various embodiments of the present inventionhave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments disclosed. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope and spirit of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application or technicalimprovement over technologies found in the marketplace, or to enableothers of ordinary skill in the art to understand the embodimentsdisclosed herein.

The present invention may be a system, a method, and/or a computerprogram product. The computer program product may include a computerreadable storage medium (or media) having computer readable programinstructions thereon for causing a processor to carry out aspects of thepresent invention.

The computer readable storage medium can be a tangible device that canretain and store instructions for use by an instruction executiondevice. The computer readable storage medium may be, for example, but isnot limited to, an electronic storage device, a magnetic storage device,an optical storage device, an electromagnetic storage device, asemiconductor storage device, or any suitable combination of theforegoing. A non-exhaustive list of more specific examples of thecomputer readable storage medium includes the following: a portablecomputer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a static random access memory (SRAM), a portablecompact disc read-only memory (CD-ROM), a digital versatile disk (DVD),a memory stick, a floppy disk, a mechanically encoded device such aspunch-cards or raised structures in a groove having instructionsrecorded thereon, and any suitable combination of the foregoing. Acomputer readable storage medium, as used herein, is not to be construedas being transitory signals per se, such as radio waves or other freelypropagating electromagnetic waves, electromagnetic waves propagatingthrough a waveguide or other transmission media (e.g., light pulsespassing through a fiber-optic cable), or electrical signals transmittedthrough a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network may comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device.

Computer readable program instructions for carrying out operations ofthe present invention may be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, or either source code or object code written in anycombination of one or more programming languages, including an objectoriented programming language such as Smalltalk, C++ or the like, andconventional procedural programming languages, such as the “C”programming language or similar programming languages. The computerreadable program instructions may execute entirely on the user'scomputer, partly on the user's computer, as a stand-alone softwarepackage, partly on the user's computer and partly on a remote computeror entirely on the remote computer or server. In the latter scenario,the remote computer may be connected to the user's computer through anytype of network, including a local area network (LAN) or a wide areanetwork (WAN), or the connection may be made to an external computer(for example, through the Internet using an Internet Service Provider).In some embodiments, electronic circuitry including, for example,programmable logic circuitry, field-programmable gate arrays (FPGA), orprogrammable logic arrays (PLA) may execute the computer readableprogram instructions by utilizing state information of the computerreadable program instructions to personalize the electronic circuitry,in order to perform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions.

These computer readable program instructions may be provided to aprocessor of a general purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks. These computer readable program instructionsmay also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus, and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowchart and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the block may occur out of theorder noted in the figures. For example, two blocks shown in successionmay, in fact, be executed substantially concurrently, or the blocks maysometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

It is understood in advance that although this disclosure includes adetailed description on cloud computing, implementation of the teachingsrecited herein are not limited to a cloud computing environment. Rather,embodiments of the present invention are capable of being implemented inconjunction with any other type of computing environment now known orlater developed.

Cloud computing is a model of service delivery for enabling convenient,on-demand network access to a shared pool of configurable computingresources (e.g. networks, network bandwidth, servers, processing,memory, storage, applications, virtual machines, and services) that canbe rapidly provisioned and released with minimal management effort orinteraction with a provider of the service. This cloud model may includeat least five characteristics, at least three service models, and atleast four deployment models.

Characteristics are as follows:

On-demand self-service: a cloud consumer can unilaterally provisioncomputing capabilities, such as server time and network storage, asneeded automatically without requiring human interaction with theservice's provider.

Broad network access: capabilities are available over a network andaccessed through standard mechanisms that promote use by heterogeneousthin or thick client platforms (e.g., mobile phones, laptops, and PDAs).

Resource pooling: the provider's computing resources are pooled to servemultiple consumers using a multi-tenant model, with different physicaland virtual resources dynamically assigned and reassigned according todemand. There is a sense of location independence in that the consumergenerally has no control or knowledge over the exact location of theprovided resources but may be able to specify location at a higher levelof abstraction (e.g., country, state, or datacenter).

Rapid elasticity: capabilities can be rapidly and elasticallyprovisioned, in some cases automatically, to quickly scale out andrapidly released to quickly scale in. To the consumer, the capabilitiesavailable for provisioning often appear to be unlimited and can bepurchased in any quantity at any time.

Measured service: cloud systems automatically control and optimizeresource use by leveraging a metering capability at some level ofabstraction appropriate to the type of service (e.g., storage,processing, bandwidth, and active user accounts). Resource usage can bemonitored, controlled, and reported providing transparency for both theprovider and consumer of the utilized service.

Service Models are as follows:

Software as a Service (SaaS): the capability provided to the consumer isto use the provider's applications running on a cloud infrastructure.The applications are accessible from various client devices through athin client interface such as a web browser (e.g., web-based e-mail).The consumer does not manage or control the underlying cloudinfrastructure including network, servers, operating systems, storage,or even individual application capabilities, with the possible exceptionof limited user-specific application configuration settings.

Platform as a Service (PaaS): the capability provided to the consumer isto deploy onto the cloud infrastructure consumer-created or acquiredapplications created using programming languages and tools supported bythe provider. The consumer does not manage or control the underlyingcloud infrastructure including networks, servers, operating systems, orstorage, but has control over the deployed applications and possiblyapplication hosting environment configurations.

Infrastructure as a Service (IaaS): the capability provided to theconsumer is to provision processing, storage, networks, and otherfundamental computing resources where the consumer is able to deploy andrun arbitrary software, which can include operating systems andapplications. The consumer does not manage or control the underlyingcloud infrastructure but has control over operating systems, storage,deployed applications, and possibly limited control of select networkingcomponents (e.g., host firewalls).

Deployment Models are as follows:

Private cloud: the cloud infrastructure is operated solely for anorganization. It may be managed by the organization or a third party andmay exist on-premises or off-premises.

Community cloud: the cloud infrastructure is shared by severalorganizations and supports a specific community that has shared concerns(e.g., mission, security requirements, policy, and complianceconsiderations). It may be managed by the organizations or a third partyand may exist on-premises or off-premises.

Public cloud: the cloud infrastructure is made available to the generalpublic or a large industry group and is owned by an organization sellingcloud services.

Hybrid cloud: the cloud infrastructure is a composition of two or moreclouds (private, community, or public) that remain unique entities butare bound together by standardized or proprietary technology thatenables data and application portability (e.g., cloud bursting forload-balancing between clouds).

A cloud computing environment is service oriented with a focus onstatelessness, low coupling, modularity, and semantic interoperability.At the heart of cloud computing is an infrastructure comprising anetwork of interconnected nodes.

Referring now to FIG. 9, a schematic of an example of a cloud computingnode is shown. Cloud computing node 10 is only one example of a suitablecloud computing node and is not intended to suggest any limitation as tothe scope of use or functionality of embodiments of the inventiondescribed herein. Regardless, cloud computing node 10 is capable ofbeing implemented and/or performing any of the functionality set forthhereinabove.

In cloud computing node 10 there is a computer system/server 12, whichis operational with numerous other general purpose or special purposecomputing system environments or configurations. Examples of well-knowncomputing systems, environments, and/or configurations that may besuitable for use with computer system/server 12 include, but are notlimited to, personal computer systems, server computer systems, thinclients, thick clients, hand-held or laptop devices, multiprocessorsystems, microprocessor-based systems, set top boxes, programmableconsumer electronics, network PCs, minicomputer systems, mainframecomputer systems, and distributed cloud computing environments thatinclude any of the above systems or devices, and the like.

Computer system/server 12 may be described in the general context ofcomputer system-executable instructions, such as program modules, beingexecuted by a computer system. Generally, program modules may includeroutines, programs, objects, components, logic, data structures, and soon that perform particular tasks or implement particular abstract datatypes. Computer system/server 12 may be practiced in distributed cloudcomputing environments where tasks are performed by remote processingdevices that are linked through a communications network. In adistributed cloud computing environment, program modules may be locatedin both local and remote computer system storage media including memorystorage devices.

As shown in FIG. 9, computer system/server 12 in cloud computing node 10is shown in the form of a general-purpose computing device. Thecomponents of computer system/server 12 may include, but are not limitedto, one or more processors or processing units 16, a system memory 28,and a bus 18 that couples various system components including systemmemory 28 to processor 16.

Bus 18 represents one or more of any of several types of bus structures,including a memory bus or memory controller, a peripheral bus, anaccelerated graphics port, and a processor or local bus using any of avariety of bus architectures. By way of example, and not limitation,such architectures include Industry Standard Architecture (ISA) bus,Micro Channel Architecture (MCA) bus, Enhanced ISA (EISA) bus, VideoElectronics Standards Association (VESA) local bus, and PeripheralComponent Interconnects (PCI) bus.

Computer system/server 12 typically includes a variety of computersystem readable media. Such media may be any available media that isaccessible by computer system/server 12, and it includes both volatileand non-volatile media, removable and non-removable media.

System memory 28 can include computer system readable media in the formof volatile memory, such as random access memory (RAM) 30 and/or cachememory 32. Computer system/server 12 may further include otherremovable/non-removable, volatile/non-volatile computer system storagemedia. By way of example only, storage system 34 can be provided forreading from and writing to a non-removable, non-volatile magnetic media(not shown and typically called a “hard drive”). Although not shown, amagnetic disk drive for reading from and writing to a removable,non-volatile magnetic disk (e.g., a “floppy disk”), and an optical diskdrive for reading from or writing to a removable, non-volatile opticaldisk such as a CD-ROM, DVD-ROM or other optical media can be provided.In such instances, each can be connected to bus 18 by one or more datamedia interfaces. As will be further depicted and described below,memory 28 may include at least one program product having a set (e.g.,at least one) of program modules that are configured to carry out thefunctions of embodiments of the invention.

Program/utility 40, having a set (at least one) of program modules 42,may be stored in memory 28 by way of example, and not limitation, aswell as an operating system, one or more application programs, otherprogram modules, and program data. Each of the operating system, one ormore application programs, other program modules, and program data orsome combination thereof, may include an implementation of a networkingenvironment. Program modules 42 generally carry out the functions and/ormethodologies of embodiments of the invention as described herein.

Computer system/server 12 may also communicate with one or more externaldevices 14 such as a keyboard, a pointing device, a display 24, etc.;one or more devices that enable a user to interact with computersystem/server 12; and/or any devices (e.g., network card, modem, etc.)that enable computer system/server 12 to communicate with one or moreother computing devices. Such communication can occur via Input/Output(I/O) interfaces 22. Still yet, computer system/server 12 cancommunicate with one or more networks such as a local area network(LAN), a general wide area network (WAN), and/or a public network (e.g.,the Internet) via network adapter 20. As depicted, network adapter 20communicates with the other components of computer system/server 12 viabus 18. It should be understood that although not shown, other hardwareand/or software components could be used in conjunction with computersystem/server 12. Examples, include, but are not limited to: microcode,device drivers, redundant processing units, external disk drive arrays,RAID systems, tape drives, and data archival storage systems, etc.

Referring now to FIG. 10, an illustrative cloud computing environment 50is depicted. As shown, cloud computing environment 50 comprises one ormore cloud computing nodes 10 with which local computing devices used bycloud consumers, such as, for example, personal digital assistant (PDA)or cellular telephone 54A, desktop computer 54B, laptop computer 54C,and/or automobile computer system 54N may communicate. Nodes 10 maycommunicate with one another. They may be grouped (not shown) physicallyor virtually, in one or more networks, such as Private, Community,Public, or Hybrid clouds as described hereinabove, or a combinationthereof. This allows cloud computing environment 50 to offerinfrastructure, platforms and/or software as services for which a cloudconsumer does not need to maintain resources on a local computingdevice. It is understood that the types of computing devices 54A-N shownin FIG. 10 are intended to be illustrative only and that computing nodes10 and cloud computing environment 50 can communicate with any type ofcomputerized device over any type of network and/or network addressableconnection (e.g., using a web browser).

Referring now to FIG. 11, a set of functional abstraction layersprovided by cloud computing environment 50 (FIG. 10) is shown. It shouldbe understood in advance that the components, layers, and functionsshown in FIG. 11 are intended to be illustrative only and embodiments ofthe invention are not limited thereto. As depicted, the following layersand corresponding functions are provided:

Hardware and software layer 60 includes hardware and softwarecomponents. Examples of hardware components include: mainframes 61; RISC(Reduced Instruction Set Computer) architecture based servers 62;servers 63; blade servers 64; storage devices 65; and networks andnetworking components 66. In some embodiments, software componentsinclude network application server software 67 and database software 68.Virtualization layer 70 provides an abstraction layer from which thefollowing examples of virtual entities may be provided: virtual servers71; virtual storage 72; virtual networks 73, including virtual privatenetworks; virtual applications and operating systems 74; and virtualclients 75.

In one example, management layer 80 may provide the functions describedbelow. Resource provisioning 81 provides dynamic procurement ofcomputing resources and other resources that are utilized to performtasks within the cloud computing environment. Metering and Pricing 82provide cost tracking as resources are utilized within the cloudcomputing environment, and billing or invoicing for consumption of theseresources. In one example, these resources may comprise applicationsoftware licenses. Security provides identity verification for cloudconsumers and tasks, as well as protection for data and other resources.User portal 83 provides access to the cloud computing environment forconsumers and system administrators. Service level management 84provides cloud computing resource allocation and management such thatrequired service levels are met. Service Level Agreement (SLA) planningand fulfillment 85 provide pre-arrangement for, and procurement of,cloud computing resources for which a future requirement is anticipatedin accordance with an SLA.

Workloads layer 90 provides examples of functionality for which thecloud computing environment may be utilized. Examples of workloads andfunctions which may be provided from this layer include: mapping andnavigation 91; software development and lifecycle management 92; virtualclassroom education delivery 93; data analytics processing 94;transaction processing 95; and mobile desktop 96.

Referring to FIG. 12, there is shown an example of a hardwareconfiguration of a computer 900 able to implement the exemplaryembodiments. As shown in the figure, the computer 900 may include acentral processing unit (CPU) 900 a serving as one example of aprocessor, a main memory 900 b connected to the CPU 900 a via amotherboard (M/B) chip set 900 c and serving as one example of a memory,and a display driver 900 d connected to the CPU 900 a via the same M/Bchip set 900 c. A network interface 900 f, magnetic disk device 900 g,audio driver 900 h, and keyboard/mouse 900 i are also connected to theM/B chip set 900 c via a bridge circuit 900 e.

In FIG. 12, the various configurational elements are connected viabuses. For example, the CPU 900 a and the M/B chip set 900 c, and theM/B chip set 900 c and the main memory 900 b are connected via CPUbuses, respectively. Also, the M/B chip set 900 c and the display driver900 d may be connected via an accelerated graphics port (AGP). However,when the display driver 900 d includes a PCI express-compatible videocard, the M/B chip set 900 c and the video card are connected via a PCIexpress (PCIe) bus. Also, when the network interface 900 f is connectedto the bridge circuit 900 e, a PCI Express may be used for theconnection, for example. For connecting the magnetic disk device 900 gto the bridge circuit 900 e, a serial AT attachment (ATA), aparallel-transmission ATA, or peripheral components interconnect (PCI)may be used. For connecting the keyboard/mouse 900 i to the bridgecircuit 900 e, a universal serial bus (USB) may be used.

Here, the present invention may be realized using all hardware or allsoftware. It can also be realized using a combination of both hardwareand software. The present invention may also be realized as a computer,data processing system, or computer program product. The computerprogram product may be stored and distributed on a non-transitorycomputer-readable medium. Here, the medium may be an electronic,magnetic, optical, electromagnetic, infrared, or semiconductor system(device or equipment), or a transmission medium. Examples of thenon-transitory computer-readable medium include semiconductors,solid-state storage devices, magnetic tape, removable computerdiskettes, random-access memory (RAM), read-only memory (ROM), rigidmagnetic disks, and optical disks. Examples of optical disks at thepresent time include compact disk read-only memory (CD-ROM) disks,compact disk read/write (CD-R/W) disks, and DVDs.

The present invention has been explained above using an embodiment, butthe technical scope of the present invention is not limited in any wayby this exemplary embodiment. It should be clear to a person of skill inthe art that various modifications and substitutions can be made withoutdeparting from the spirit and scope of the present invention.

What is claimed is:
 1. A computer-implemented method for computing anintersection or an intersection cardinality of each pair of a set in afirst list of a plurality of sets and a set in a second list of aplurality of sets, the method comprising: calculating a first union of apredetermined number of sets in the first list; obtaining filtered setsof the second list by filtering out an element from the plurality ofsets in the second list, the element being not included in the firstunion; and intersecting a set in the first list and a set in thefiltered sets of the second list.
 2. The method according to claim 1,wherein the predetermined number of sets is proportional to(|D|/|C|)^(1/2), where |D| represents a number of all possible elementsof each set, and |C| represents the size of the largest set among thepredetermined number of sets or the size of a set having an average sizein the predetermined number of sets.
 3. The method according to claim 2,wherein the sets in the first list are listed in the order of size, andthe predetermined number of sets are selected in order from thebeginning of the first list.
 4. The method according to claim 1, whereinthe predetermined number of sets is selected such that the size of thefirst union is smaller than the number of all possible elements of eachset and larger than the size of each set.
 5. The method according toclaim 1, wherein the intersecting a set in the first list and a set inthe filtered sets of the second list is performed on condition that thesize of the first union is a predetermined size and over.
 6. Acomputer-implemented method for computing an intersection or anintersection cardinality of each pair of a set in a first list of aplurality of sets and a set in a second list of a plurality of sets, themethod comprising: calculating a first union of a predetermined numberof sets in the first list; obtaining filtered sets of the second list byfiltering out an element from the plurality of sets in the second list,the element being not included in the first union; calculating a secondunion of a predetermined number of sets in the second list; obtainingfiltered sets of the first list by filtering out an element from theplurality of sets in the first list, the element being not included inthe second union; and intersecting a set in the filtered sets of thefirst list and a set in the filtered sets of the second list.
 7. Themethod according to claim 6, wherein the sets in the first list and thesets in the second list are respectively listed in the order of size andthe predetermined number of sets in the first list and the predeterminednumber of sets in the second list are respectively selected in orderfrom the beginning of the first list and from the beginning of thesecond list.
 8. The method according to claim 6, wherein intersecting aset in the filtered sets of the first list and a set in the filteredsets of the second list is performed on condition that the size of thefirst union is a predetermined size and over and the size of the secondunion is a different predetermined size and over.
 9. A system forcomputing an intersection or an intersection cardinality of each pair ofa set in a first list of a plurality of sets and a set in a second listof a plurality of sets, the system comprising a processor and a memorycoupled to the processor, wherein the memory comprises instructionswhich, when executed by the processor, cause the processor to: calculatea first union of a predetermined number of sets in the first list;obtain filtered sets of the second list by filtering out an element fromthe plurality of sets in the second list, the element being not includedin the first union; and intersect a set in the first list and a set inthe filtered sets of the second list.
 10. The system according to claim9, wherein the predetermined number of sets is proportional to(|D|/|C|)^(1/2), where |D| represents a number of all possible elementsof each set, and |C| represents the size of the largest set among thepredetermined number of sets or the size of a set having an average sizein the predetermined number of sets.
 11. The system according to claim10, wherein the sets in the first list are listed in the order of size,and the predetermined number of sets are selected in order from thebeginning of the first list.
 12. The system according to claim 9,wherein the predetermined number of sets is selected such that the sizeof the first union is smaller than the number of all possible elementsof each set and larger than the size of each set.
 13. The systemaccording to claim 9, wherein the memory comprises instructions whichcause the processor to intersect a set in the first list and a set inthe filtered sets of the second list on condition that the size of thefirst union is a predetermined size and over.
 14. A computer programproduct for computing an intersection or an intersection cardinality ofeach pair of a set in a first list of a plurality of sets and a set in asecond list of a plurality of sets, the computer program productcomprising a computer readable storage medium having programinstructions embodied therewith, the program instructions executable bya computer to cause the computer to: calculate a first union of apredetermined number of sets in the first list; obtain filtered sets ofthe second list by filtering out an element from the plurality of setsin the second list, the element being not included in the first union;and intersect a set in the first list and a set in the filtered sets ofthe second list.
 15. The computer program product according to claim 14,wherein the predetermined number of sets is proportional to(|D|/|C|)^(1/2), where |D| represents a number of all possible elementsof each set, and |C| represents the size of the largest set among thepredetermined number of sets or the size of a set having an average sizein the predetermined number of sets.
 16. The computer program productaccording to claim 15, wherein the sets in the first list are listed inthe order of size, and the predetermined number of sets are selected inorder from the beginning of the first list.
 17. The computer programproduct according to claim 14, wherein the predetermined number of setsis selected such that the size of the first union is smaller than thenumber of all possible elements of each set and larger than the size ofeach set.
 18. The computer program product according to claim 14,wherein the program instructions executable by a computer cause thecomputer to intersect a set in the first list and a set in the filteredsets of the second list on condition that the size of the first union isa predetermined size and over.